In each even of gold collisions only a few thousand particles at most are created, so it's not possible to reconstruct the temperature fluctuations on the surface of last scattering for an individual collision in the same way that it is done with the Cosmic Microwave Background. To search for evidence of hotspots, we must instead look to measurements that can be accumulated over thousands, millions, or even billions of collisions. The data we use was published by the STAR collaboration in 2006 [1]. The correlations shown in this data are derived by studying how the fluctuations in the mean transverse momentum change depending on the width of the region we look at. This would be analogous to studying the temperature fluctuations of the cosmic microwave background by looking at millions of different universes and measuring how the average temperature changes depending on how much of the sky we look at. That information can be converted to information about how correlated on average, one part of the sky is with another part at some distance away. That is what is shown in the figure except for tracks in the detector, not spots in the sky. The figure says that when particles have above average momentum, nearby particles also have momentum above average. This is what we would expect from hotspots. The hot-spots decay into clusters of particles that tend to be more energetic because of the higher temperature of the hotspot.
And to determine the sound from this data we first determined the power spectrum.